Constructing linked systems of relative difference sets via Schur rings

Mikhail Muzychuk; Grigory Ryabov

doi:10.1007/s10623-024-01406-w

Constructing linked systems of relative difference sets via Schur rings

Mikhail Muzychuk, Grigory Ryabov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In the present paper, we study relative difference sets (RDSs) and linked systems of them. It is shown that a closed linked system of RDSs is always graded by a group. Based on this result, we also define a product of RDS linked systems sharing the same grading group. Further, we generalize the Davis-Polhill-Smith construction of a linked system of RDSs. Finally, we construct new linked system of RDSs in a Heisenberg group over a finite field and family of RDSs in an extraspecial p-group of exponent p². All constructions of new RDSs and their linked systems make usage of cyclotomic Schur rings.

Original language	English
Pages (from-to)	2615-2637
Number of pages	23
Journal	Designs, Codes, and Cryptography
Volume	92
Issue number	9
DOIs	https://doi.org/10.1007/s10623-024-01406-w
State	Published - 1 Sep 2024

Keywords

05B10
05E30
20C05
Linked systems
Relative difference sets
Schur rings

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science Applications
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/s10623-024-01406-w

Cite this

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AU - Ryabov, Grigory

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Constructing linked systems of relative difference sets via Schur rings

Abstract

Keywords

ASJC Scopus subject areas

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